# Trapezium - Formula, Area of a Trapezium and Perimeter of a Trapezium

Trapezium, as defined by the Euclidean geometry, is a four-sided figure which contains a pair of parallel sides opposite to each other and another pair of non-parallel sides also opposite to each other. The term Trapezium has its origins in the Greek language from the word ‘trapeza’, meaning a table. Since a trapezium looks like a table.

A trapezium comes under the 2D geometric figures and is a special case of quadrilaterals. Until now, we have only learned about regular quadrilaterals having opposite sides parallel, the trapezium is the only quadrilateral whose one pair meets, and the other one does not. The sides which don’t meet each other are termed as the bases of the trapezium, while the ones which meet are termed as the legs of the same trapezium. The trapezium is also known as trapezoid and is a completely closed shaping having four vertices and two diagonals. Interestingly, the diagonals of a trapezium are of equal size. The adjacent angles inside the trapezium will always sum up to form supplementary angles (180-degrees), and the sum of all the interior angles is the complete angle (360-degrees). The line connecting the center point of the non-parallel sides will always be parallel to the bases or parallel sides and identical to half of the total of parallel sides. You can find trapezium-shaped objects everywhere, from your popcorn bucket to the table lamp shed, from your buckets to tabletops. This shape is classified into three major types:

Isosceles Trapezium: In these types of trapeziums, the legs of the figure are identical or have an equal length, just like an isosceles triangle. Scalene Trapezium: It is defined as a trapezium that constitutes the sides of distinct sizes. All four lengths are of different dimensions. Right-angled Trapezium: In this type of trapezium, one of the legs of the trapezium makes right angles with both the parallel bases of the shape. The 2nd leg is still at some angle from the bases.

## Area of a Trapezium

The area of the trapezium is the area covered by a face of a trapezium figure in 2D space or the coordinate plane. The surface area is calculated by the figure's two parallel sides known as the bases and the maximum height of the shape. The height is calculated by extending a direct perpendicular line from the apex of one base to the other. The height of the trapezium is then determined using Pythagoras' theorem (because the perpendicular makes a right-angle triangle). The area of any trapezium object is calculated using the formula:

Area = (1/2) x (a1 + a2) x d, a1 and a2 are the lengths of parallel bases, and ‘d’ is the height of the trapeze object.

## The Perimeter of a Trapezium

The perimeter of a trapezium is defined as the total distance covered along the dimension of the figure. It can also be defined as the sum of all the lengths of the trapezium. The perimeter of a trapezium PQRS is formulated as PQ + QR + RS + QS. For example, if the trapezium is an isosceles trapezium, then the perimeter is given as a + b + 2c, where ‘a’ and ‘b’ are lengths of parallel sides, and c is the length of the equal legs.